Active Transport is a process by which ions or molecules move against a concentration gradient; in other words, moving towards an area where there are already numbers of ions or molecules. This process is the opposite of Diffusion, or Passive Transport, where they move from a concentrated area to a less concentrated area. Diffusion takes no energy to perform, Active Transport, as the name implies, requires energy.
Primary Active Transport uses energy stored in the ATP molecule to drive a sodium/potassium "pump" which moves sodium ions out of a cell, and moves potassium ions into the cell. The result is that there's a high concentration of potassium, and low concentration of sodium inside the cell. The reverse is found outside the cell -- a high concentration of sodium, and a low concentration of potassium.
Secondary Active Transport does not use an ATP driven pump; instead, it employs carrier proteins to move the required ions or molecules across the cell membrane.